/*===========================================================================
 
 Copyright (C) 2000-2012 Yves Renard
 
 This file is a part of GETFEM++
 
 Getfem++  is  free software;  you  can  redistribute  it  and/or modify it
 under  the  terms  of the  GNU  Lesser General Public License as published
 by  the  Free Software Foundation;  either version 3 of the License,  or
 (at your option) any later version along with the GCC Runtime Library
 Exception either version 3.1 or (at your option) any later version.
 This program  is  distributed  in  the  hope  that it will be useful,  but
 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 or  FITNESS  FOR  A PARTICULAR PURPOSE.  See the GNU Lesser General Public
 License and GCC Runtime Library Exception for more details.
 You  should  have received a copy of the GNU Lesser General Public License
 along  with  this program;  if not, write to the Free Software Foundation,
 Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301, USA.
 
===========================================================================*/



#include "getfem/bgeot_poly.h"
#include "getfem/bgeot_vector.h"
#include "getfem/bgeot_ftool.h"

namespace bgeot {

#define STORED 150
  static gmm::dense_matrix<size_type> alpha_M_(STORED, STORED);
  static void alpha_init_() {
    static bool init = false;
    if (!init) {
      for (short_type i = 0; i < STORED; ++i) {
	alpha_M_(i, 0) = alpha_M_(0, i) = 1;
	for (short_type j = 1; j <= i; ++j)
	  alpha_M_(i,j) = alpha_M_(j,i) = (alpha_M_(i, j-1) * (i+j)) / j;
      }
      init = true;
    }
  }
  static inline size_type alpha_(short_type n, short_type d)
  { return alpha_M_(d,n); }

  size_type alpha(short_type n, short_type d) {
    alpha_init_();
    GMM_ASSERT1(n < STORED && d < STORED,
		"alpha called with n = " << n << " and d = " << d);
    return alpha_(n,d);
  }

  const power_index &power_index::operator ++() {
    short_type n = short_type(size()), l;
    if (n > 0) {
      size_type g_idx = global_index_; short_type deg = degree_;
      reverse_iterator it = rbegin() + 1;
      for (l = short_type(n-2); l != short_type(-1); --l, ++it)
	if (*it != 0) break;
      short_type a = (*this)[n-1]; (*this)[n-1] = 0;
      (*this)[short_type(l+1)] = short_type(a + 1);
      if (l != short_type(-1)) ((*this)[l])--;
      else if (short_type(deg+1)) degree_ = short_type(deg+1);
      if (g_idx+1) global_index_ = g_idx+1;
      //degree_ = short_type(-1);
    }
    return *this;
  }
  
  const power_index &power_index::operator --() {
    short_type n = short_type(size()), l;
    if (n > 0) {
      size_type g_idx = global_index_; short_type deg = degree_;
      reverse_iterator it = rbegin();
      for (l = short_type(n-1); l != short_type(-1); --l, ++it) {
	if (*it != 0) break;
      }
      if (l != short_type(-1)) {
	short_type a = (*this)[l];
	(*this)[l] = 0; (*this)[n-1] = short_type(a - 1);
	if (l > 0) ((*this)[l-1])++; 
        else if (short_type(deg+1)) degree_ = short_type(deg-1);
      }
      if (g_idx+1) global_index_ = g_idx-1;
    }
    return *this;
  }
  
  short_type power_index::degree() const {
    if (degree_ != short_type(-1)) return degree_;
    degree_ = short_type(std::accumulate(begin(), end(), 0)); 
    return degree_;
  }

  size_type power_index::global_index(void) const {
    if (global_index_ != size_type(-1)) return global_index_;
    short_type d = degree(), n = short_type(size());
    global_index_ = 0;
    const_iterator it = begin(), ite = end();
    for ( ; it != ite && d > 0; ++it)
      { global_index_ += alpha_(n,short_type(d-1)); d=short_type(d-*it); --n; }
    return global_index_;
  }
 
  power_index::power_index(short_type nn) : v(nn), degree_(0), global_index_(0)
  { std::fill(begin(), end(), short_type(0)); alpha_init_(); }


  // functions to read a polynomial on a stream

  static void parse_error(int i)
  { GMM_ASSERT1(false, "Syntax error reading a polynomial " << i); }

  static std::string stored_s;
  int stored_tokent;

  static void unget_token(int i, std::string s)
  { stored_s = s; stored_tokent = i; }

  static int get_next_token(std::string &s, std::istream &f) {
    if (stored_s.size() == 0)
      return get_token(f, s, true, false, false);
    else { s = stored_s; stored_s.clear(); return stored_tokent; }
  }

  static base_poly read_expression(short_type n, std::istream &f) {
    gmm::stream_standard_locale sl(f);
    gmm::standard_locale sll;
    
    base_poly result(n,0);
    std::string s;
    int i = get_next_token(s, f), j;
    switch (i) {
    case 2 : result.one();
      result *= opt_long_scalar_type(::strtod(s.c_str(), 0));
      break;
    case 4 :
      if (s == "x") result = base_poly(n, 1, 0);
      else if (s == "y" && n > 1) result = base_poly(n, 1, 1);
      else if (s == "z" && n > 2) result = base_poly(n, 1, 2);
      else if (s == "w" && n > 3) result = base_poly(n, 1, 3);
      else if (s == "v" && n > 4) result = base_poly(n, 1, 4);
      else if (s == "u" && n > 5) result = base_poly(n, 1, 5);
      else if (s == "t" && n > 6) result = base_poly(n, 1, 6);
      else if (s == "sqrt") {
	base_poly p = read_expression(n, f);
	if (p.degree() > 0) parse_error(1);
	result.one();  result *= sqrt(p[0]);
      }
      else parse_error(2);
      break;
    case 5 :
      switch (s[0]) {
      case '(' :
	result = read_base_poly(n, f);
	j = get_next_token(s, f);
	if (j != 5 || s[0] != ')') parse_error(3);
	break;
	default : parse_error(4);
      }
      break;
    default : parse_error(5);
    }
    return result;
  }

  static void operator_priority_(int i, char c, int &prior, int &op) {
    if (i == 5)
      switch (c) {
      case '*' : prior = 2; op = 1; return;
      case '/' : prior = 2; op = 2; return;
      case '+' : prior = 3; op = 3; return;
      case '-' : prior = 3; op = 4; return;
      case '^' : prior = 1; op = 5; return;
      }
    prior = op = 0;
  }

  void do_bin_op(std::vector<base_poly> &value_list,
		 std::vector<int> &op_list,
		 std::vector<int> &prior_list) {
    base_poly &p2 = *(value_list.rbegin());
    if (op_list.back() != 6) {
      assert(value_list.size()>1);
      base_poly &p1 = *(value_list.rbegin()+1);    
      switch (op_list.back()) {
        case 1  : p1 *= p2; break;
        case 2  : if (p2.degree() > 0) parse_error(6); p1 /= p2[0]; break;
        case 3  : p1 += p2; break;
        case 4  : p1 -= p2; break;
        case 5  : 
	  {
	    if (p2.degree() > 0) parse_error(7);
	    int pow = int(to_scalar(p2[0]));
	    if (p2[0] !=  opt_long_scalar_type(pow) || pow < 0) parse_error(8);
	    base_poly p = p1; p1.one();
	    for (int i = 0; i < pow; ++i) p1 *= p;
	  }
	  break;
        default: assert(0);
      }
      value_list.pop_back(); 
    } else {
      p2 *= opt_long_scalar_type(-1);
    }
    op_list.pop_back(); prior_list.pop_back();
  }

  base_poly read_base_poly(short_type n, std::istream &f) {
    std::vector<base_poly> value_list;
    std::string s;
    std::vector<int> op_list, prior_list;
    
    int i = get_next_token(s, f), prior, op;
    if (i == 5 && s[0] == '-')
      { op_list.push_back(6); prior_list.push_back(2); }
    else if (i == 5 && s[0] == '+') ;
    else unget_token(i, s);

    value_list.push_back(read_expression(n, f));
    i = get_next_token(s, f);
    operator_priority_(i, s[0], prior, op);
    while (op) {
      while (!prior_list.empty() && prior_list.back() <= prior)
	do_bin_op(value_list, op_list, prior_list);

      value_list.push_back(read_expression(n, f));
      op_list.push_back(op);
      prior_list.push_back(prior);
      
      i = get_next_token(s, f);
      operator_priority_(i, s[0], prior, op);
    }
    
    if (i == 5 && s[0] == ')') { f.putback(')'); }
    else if (i != 0 && (i != 5 || s[0] != ';')) {
      cout << "s = " << s << endl;
      parse_error(9);
    }

    while (!prior_list.empty()) do_bin_op(value_list, op_list, prior_list);

    return value_list[0];
  }

  base_poly read_base_poly(short_type n, const std::string &s)
  { std::stringstream f(s); return read_base_poly(n, f); }


}  /* end of namespace bgeot.                                             */
